Rock is not carbon dated. C14 has a half life of about 6000 years; radioisotope dating is mostly accurate within the first 6 or so half lifes (~36,000 years for C14). Also, you have to remember, that even if the volcano erupted 200 years ago, the rock that emerged is as old as the earth.
As old as the earth? Why stop there? We’re talking formerly molten lava, here. I though argon was supposed to be the problem, making it look “too old.”